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The Collaborative International Dictionary
incompetible

Incompatible \In`com*pat"i*ble\, a. [Pref. in- not + compatible: cf. F. incompatible.] [It was formerly sometimes written incompetible.]

  1. Not compatible; so differing as to be incapable of harmonious combination or coexistence; inconsistent in thought or being; irreconcilably disagreeing; as, persons of incompatible tempers; incompatible colors, desires, ambition.

    A strength and obduracy of character incompatible with his meek and innocent nature.
    --Southey.

  2. (Chem.) Incapable of being together without mutual reaction or decomposition, as certain medicines.

    Incompatible terms (Logic), terms which can not be combined in thought.

    Syn: Inconsistent; incongruous; dissimilar; irreconcilable; unsuitable; disagreeing; inharmonious; discordant; repugnant; contradictory. See Inconsistent.

Wiktionary
incompetible

a. 1 (context obsolete English) Outside of one's competence 2 (archaic form of incompatible English)